Microwave filter



Feb- 6, 1951 w. w. MUMFORD 2,540,488

MICROWAVE FILTER Filed April 30, 1948 3 Sheets-Sheet 2 |00 TANDNG WA VE RATIO W. W. MUMFORD BV ATTORNEY Feb. 6, 1951 W, W, MUMFORD 2,540,488

MICROWAVE FILTER Filed April 50, 1948 5 Sheets-Sheet 5 as 24 S20 l5 o I I I l O D o o C o o N m In (D l` Q O O o O O O O v v v v v v v FREQUENCY- MGCYC/ E` F f6. /3 F/G. /4

a a. l bl* /6 VVE/WOA By W. W. MUM/:ORD

. n W ZM ATTORNEY Patented Feb. 6, 1951 MICROWAVE FILTER William W. Mumford, Atlantic Highlands, N. J.,

assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application April so, 194s, serial No. 24,257 Y (ci. 17a-44) 24 Claims.

k'Ihis invention relates to frequencyselective networks and more particularly to microwave filters for use in wave guides.

" The principal object of the invention is toV im'p'rove Vthe transmission characteristics of microwave filters. A more specic object is t equalize fthe insertion loss and minimize the eilection coeicient of such a filter over a'wide and.

"e In many applications it is desirable to have a microwave filter with a substantially constant insertion' loss and a reflection coeliicient which is substantially zero over as wide a band of frequencies as possible. A filter with such a characteristic is herein called a maximally-flat lter. 'I 'his type of characteristic is of particular importance, for example, in microwave television repeaters, where'the lter may be located some distance from the receiving antenna and reflections'at thejfilter input will cause disturbing echecs- In the microwave lter in'accordance'with the present invention the insertion loss can be Ymade constant `and the reection `coeiicient Vcan be made substantially zero over. as wide a band as desired by using a sucient number of component elements. The filter comprises a plurality of resonant chambers connected in tandem by interposed sections of wave guide. In the embodiment shown each chamber is formed by a pair of substantially equal susceptive admittances positioned within a Wave guide and so spaced from each other as to define a chamber which is resonant at the mid-band frequency of the band to` be passed. This spacing is approximately a half wavelength at the Vmid-band frequencyl The admittances may, vfor example, bev

apertured transverse partitions, or irisesy or posts extendingV all Aor part of the way across the guide. It is sometimes convenient to provide means for adjusting the resonant frequency of the chamber. A tuning plug, inserted through a wall of the guide at a point intermediate the pair oi. admittances, may, for example, be used for this purpose. Adjacent chambers are connected by a section of wave guide having a length approximately equal to the average spacing of the two pairs vof admittances forming the adjacentchambers, decreased by a quarter wavelength and increased by an integral number, which may be zero, of h alf wavelengths in the guide at the midband frequency. These connecting sections are, therefore, approximately equal in length to an odd multiple, including unity, of quarter wavelengths at the resonant frequency.

, For a maximally-flat lter in accordancewith the invention, when the number of resonant chambers exceeds two the respective band widths passed by the chambers increase progressively from the centerto both ends of th'e filter. 'I'his tapering cf the pass bands is prefetably' accomplished by controlling the susceptances of the respective pairs of admittances. When irises are employed as the admittance elements, the susceptance may be controlled by the size of the" iris opening. When inductive' posts are used,

the susceptancedepends upon the cross-sectional n area and the position with respect to the longitudinal center line of the guide. For example,

the posts may all have the same diameter with' the respective pairs 'progressively displaced transversely as 'the ends of the filter are approached from the center.

The nature of the vinvention will be more fully understood from the following detailed description and by reference to the accompanying drawing in which like reference characters are used to designate similar or corresponding parts and in which:

Figs. 1, 2 and 3 are schematic filter diagrams to be referred to in developing thev design procedure for filters of the invention;

Fig. 4 is a block schematic diagram of the arrangement of elements of a filter according to the invention;

Figs. 5, 6,7 and 8 show curves useful in design- "ing a-lter according to the invention;

Fig. 9 showsaiilter -characteristic obtained with a filter constructed in accordance with the invention; f

Fig. 10 is a longitudinal sectional view of a four-branch filter in accordance with the invention employing inductive irises;

Fig. 11 is a longitudinal sectional View of another four-branchV lter in -accordance with the invention in which the susceptances are furnished by inductiveposts;

Fig. 12 shows a cross-section of the filter of Fig. 11 taken at the section line I2-I2;

Fig. 13 shows. a cross-section of the lter of Fig. 10 taken at the section line I3-I3; and

" Fig. 14 is a cross-sectional view of a modification of the lter of Fig-10, using capacitive irises.. A

Av filter generically of the type referred to above as a maximally-atlter is disclosed in UnitedStates Patent No. 1,849,656 issued March 15, 1932, to W. R. Bennett. Itis shown in the patent how to proportion the series and shunt branches from section to section to form a tapered line. structure such as to give Vthe lter as a 'wholea smooth transmission characteristic over the pass band, free from irregularities due to undamped resonances. In s uch a filter the "i bandwidth of the selective branches decreases shunt reactances, respectively inverse to each from section to section from each end of the filter to the middle, the value of the series and other, being proportional to the quantity Sill 2dr- 11' where r denotes -the order of a fbranch--(seriesorshunt) counting-frmone-Fend and-fnt isthe total number of branches.

In attempting to construct a wave guide filter-- having its reactances proportioned to provide a maximally-nat transmission characteristicl-inac'i' cordance with general design-` principles-.taught by the Bennett patent, certain-new factorscome in which raise diiculties. One of"-these-has-to do with mutual impedance between the successive branches and another has to do with the excess phase shift possessed by resonant'cavities"where these are used as the lter reactances. Y

At ordinary wire transmission frequencies where coils `and condensers are used,Y the-mutual impedance between iilter elements-can ber'made! small enough- -to rbeignored. At waveeguiderfrequencieaI-Uhowever; it is diiTicultfor-impossibletoVV isc'latev the iilterbranchesI without introducing 2O. In particular-it -isqui-te di-icult tolum-p -all vof the f desired -l'ilter branches-at onefpla-ce in-awaveguidev without encountering the complicated-effects ofY mutualimpedances,- and ifr-the` filterf branchesY are separatedby lengthseof` guide suiicient--tof` reduce the mutual impedanc'es -to--a negligibly other effects which-must be -takeninto account.

small-value these separating-lengths of guide-act as -lter- 'elements' and mustbedaccominodated Tin the over-all design. Where"the-frequencyselecV tivity introduced fby` the length of line 'inserted between fthe" ilter` branches" is'- suffi-cientA to fre-*-r quire compensation, this may be done by=bradv enin'g'- by' an'l` equivalent amount-'the l"selectivities of- -the adj acentfilterbranches.'

Resonant cavities; While {similar fbehavior' to lumpedl tuned f circuits in possessing frequency selectivefti'an'sr'nission pr'pertie's and -phase-'fshiftfserie`s"-banche's Starting at the left end of the circuit -of ILFig. 2 there is rst encountered the shunt branch 30, which? is identical -With the branch -30 of Fig. 1. Due to the impedance transforming `.property of 'the quarter-'wave sectionuli; the parallel-resonant 'shunt brar'ichv 3'l'of -Ffg.1 appears .in- Fig. 2 as the "series-resonant series branch .-3'1." The branch 32 VinFg';12undergoesfa ydouble .impedance transformation-due the twoquart'rwave sections 35 :andi 36 andthereJ-l* fore-appears in F1-ig.. Z-"in its original frm parallelresonant shunt'branch. Iii likeV unan;Y

, nerthe-shun-tbranch 3-3 of Fig..v lappearsun-A changed in Fig.- rZ'b'ut vthe branch` 3l becomes the. series-resonantseries` branch" 34l in Fig: 2.`

Ifvit-is found tha-tal quarter wavelength separc.- tion- -is insufficient toreducethe' mutual-.im-

Y peda-ncebetween Iadjacent-lter branches by the? differ in having an excess phase shftwhchcan` bef' tallzeriI into acuntn' specifying 'the lengthV of guide to be included between successive-icavities of the-suer;

In' a' -wa`ve'-vr guide lter'' of the maximally-fiat type made up of resonant cavities built-into' the Pered in accordance with" the rule given in "-Bennetts" patent', but other "critical dimensions i are (1 corrected value'of bandwith of"ca\'fitie's'to'I compensate the filter eiects introduced by the isolating lengths of guide; and (2)' corrected length of lseparating linesection to 'compensate eice/ssmphase shift o'f the 'resonantcaviti'esf In order to provide the inverse series and shiiiit reactan'ces" required "for "the lterj advantagefis take', according Vto `this invention; of "thepiiartei wavelength" line -as an impedance transfer'mer'V to supply the series reactanc'es' from thefphvsiA cally included shunt reactances in the lline'.` This'l permits constructing a waveguide filtery forv exl' ample, comprised of resonant'cavities'beh'aving as shunt resonant circuits; separated a quarterf wavelength (or oddmulti'ple thereof) apa'rt'along.'

the guideandf having` bandwidths taperedfrom section to section from'each? end of the ltertothe middle-,as-specied above. The-quarter.wavelength separating sections give the effect, .in such case, of transformingf. alternate shunt-resonantY circuits in shunt to series-resonant circuits in series in the line. Conversely, if the shunt reactances are series-resonant,V the transformed redecreasing the selectivities of the ltr branchcs'v by appropriate: amounts) f particularl-y.- in-broad bandflters-- Reference ni'ade-tofajiparticularcaseasfreps-= resented i` `3.Wherean-Tideally'inverting'line'f In" isilprov'id atfeachf end-with tuned circuit Il; IIfof trier-pro er'diinensid" orflcofripensateing lineselectivity#` over*y ai Inissiin.band-*-M Tnead-rnittanecffeach brauen-I I isf and it" remains to" determine" the selectivity "ot"-j each circuit I I under 'the'fllowin'g'specifled 'ccnl`` ditionsz' n The' circuitat A'the 'far er'idofthe"quarter W'avelength" transforming linesection is 'shown as con-- sis'tingr of Aa vparallel-resonant"circuit".I2 'andi a" terminating,.impedance I3 of admittanceiYIi terminating admittance-'fof-'" the-f. sinv f shunt' branch IZMtOgether-i with itsLtI'nin'ating-- impedance l 3 isgiVen-by.:

lis nominally a line a quarter wavelength long and A is the Wavelength.

f a(l f )(l) "6' v a Va i( 1 p f 2 Since the terminating admittance of a single oi.' selectivity as equal to img-9 (n the admittance L LO) f o f or .substituting for from Equation for the selectivity, Y.

Ifrthe connecting line is threefourths wavelength long, the correction to be applied is elf Fora lter comprising more than two-resonant chambers connected in tandem l.byvsections of wave guide, the general rule is thatA the selectivityvof each end chamber is decreased by andthe selectivity of each intermediate chamber is decreased by for every quarter. wavelength of,r length of the connecting sections, to compensateA `for the seleetlivity of the seqtionsmshln't resonant branch may be expressed in termsy 6 and solving Compensation for excess phase shift of resonant cavities Referring now to Fig. 4, a four-branch iilter is represented, comprising four resonant cavities, the end ones of which are each formed by a pair of obstacles yBl, separated a distance S1 from each other. The other or middle cavities are each formed by a pair of obstacles 7Bn separated a distance Sz from each other. Each cavity is separated from the nextl by a length of line, the section S12 separating each of the end cavities from the next and S22 separating the two middle cavities.

Considering each cavity by itself, the obstacles at each end are assumed to be equal and to have a susceptance, BYU, whereYo is the surge admittance of the connecting transmission line. This o B (l0) where Xo is the resonant Wavelength in the transmission line, Z is the length of the cavity (in Fig. 4, Si orL S2) and B is the normalized susceptance of the end obstacles.

rT his resonance occurs at anyone of a number of wavelengths at which the above relation is satisfied, but the rst and second longest wavelengths at which resonance occurs are in the region which is usually of greatest interest..

The selectivity in this region is determined also by the value of the susceptance, BYo, of the obstacles, and is given by the relation:

arc tan,

This selectivity is based upon ythe wavelength, notthe frequency parameter. In terms of the wavelength in the transmission line Vthis is Qa=27rl' (12) Where A@ isthe wavelength of resonance in the Wave guide and kga and lgcz are the wavelengths at the half power loss points, (For narrow percentage bands,lthe percentage bandwidth is greater in terms nof wavelength than in terms of frequency by the square of the ratio of the wavelengths 'in the guide and infree space.)

Fig'. 6 gives twoplots'fof this relation between selectivity and susceptance,v the curve L being for an inductive obstacle of the type shown in Figs. 12 and 13 and the curve C being for a capacitive obstacle of the type shown in Fig. 14. From the ordinate scales in Fig, 6 it is seen that the susceptance B is negative for an inductive obstacleland positivefor a'capacitive obstacle.

Ihe excess phase shift vreferred to above is taken care of by rst. representing it as a` short length, l', of transmission line and then absorbing this into the connecting linebetween cavities. This excess length of line, l', is found from the relation.

2, Mages-setz Combining b-rthis Equationzfl 0f; and-isolvingf ori' Z gives 2 v 5 whererl Vis' thelength;ofiftheifcayity; (between. itsL obstacles) Theflengtirof: connectinggline e is. a; quarter fwavelength,..orf some .odd multiple; of. a quarter Wavelength; .corrected't at one' end by elif.-

8 a post such as I9 decreases as the post is movedzv 01T center. This feature is attractive when it is desired to make all thelposts in a filter from steek of a given diameter.

A., The vcmsyel-of'f'Fig; 8 givesthevalue.;y ofizthe 1.1 parameter K for the inductive'.obstacle;showrrx:l

in Fig. 13 comprising a transverse partition 2i, having a thickness of 0.050 inch, with a centrally located rectangular-aperture of width d sorbingxair-length Zzsforxthe cavity locatedatrthatfwflfextending Completely Cross the rectangular 11H2 i' 2 4v-h2; where Z1 is the length of one cavityy and Z2 is Wave guide 20 in-a direction parallel to the electric Vector E.

The normalized susceptance B may be calculated from the parameter K, the wavelength-Air 151i in the guide, and the width a of the guide from the relationship.

L. B KazaT As an illustration of the designprocedure, the following example .is.given.. It is the objective of this design to obtain a maximally-fiat wave guide filter having a pass bandsyrnmetrically centered-:.-V at a frequency fo of 4050 megacycles and'having integer, 'includingzeros This importantlre'lationship expressed in'words means that the length of the'connecting'line' between'- tfviol resonantV cavities is" equal' toal the pass band of fo ilO megacycles and at least 28 decibels standing wave ratio outside .of.the..band;.. defined by fn iSO megacycles. The rectangular Wave guide .size .isto be 0.872 inch x 1.872 inches.

ter wavelength, to'which maybe added a half-"i wavelength orn somemultiple of a half wavelength;- y

'it' isseen fromtEfquation 13 that' thesign` of and maximally-flat, the requirements on either@ side of the* resonantv frequency maybe "usedd'to'y obtain tlie'selectivity of 4"the total lter-and the'rf number of elements that'areneeded In this l canbeplus or'minus dependingionI whether^35rzexamp1e the high frequency Side Wm be conthe susceptance 'B" of the obstacle is negative or positive. Where the obstacles, are inductive, B is negative and where-they are capacitive, B is positive. In the inductive case thezexcess phase is positive a'nd" when 'this Aris absorbed into the 4.0.-.`

connecting line thelength .of the latter is slightly 'less than a quarter wavelength or odd multiple-'there In the capacitive case V`the excessphaseisliift; is negative Vand the connecting 'line4 must be "mad'ee slightly Vgreater` than afquarter'545.4V

wavelength or odd multiple thereof.

Wave guide filter structure and design Consideration Will"rstibe given to types of andtli'is ratio in'decibelsl'is'plotted againstfiln a'sff' curve A in Fig. 5. 7? The insertion loss for this type of filter can be expressed in terms of thtotal selectivity QT by IicssifunctionLl-l-[Q'T (18) Wave guide obstacles '-that.may be used in cono-ewhere structing a lter, three of these types being slicwnin-Fig's:12;` 13and114.

While approximate formulas are"available for the'susceptance lof each of 'these'three"types-aofi" o bsta'clesf'it is necessaryjin practice'ftorusefcor- 55.C'nihg the bm laticnships were "obtained *Witl'i' rectangular *guides 55 diameter d centrally locatedY in` a,V rectangular' '10i' waveguide of width a; parallel te tliev electric' vector E of the electromagnetic waves withintl'le` guide. Fig.. l2 shows suclraninductive post I9 pcsitioned, howeverJ-Ufrfcentrfinstead of at thecenter of a Wavegide 20. The susceptance' of 75*I om The loss Aindecibelsv is plotted against si las curved' ,1 B`fin^Figf 5,"-

Inthe'illustrativedesign; let fi=fo+10 mega cycles where-'the standing wave ratio is-tobe i0. 4'? decibel'oriess'and'letifzlwo-l-30 megacycles'where'q the standing wave ratio is to be at least 28 deci-'- bels. From these two frequencies the two frequency parameters S21 and Q2 are obtained from I Arorn the original specification, and from Equation 17 (plotted as curve A in Fig. 5) the two values are obtained:

from which n=3.8, which is the least number of branches that Will meet the requirements. The next higher integer, 4, is then established as the number of branches. the general conguration .shown in Fig. 4, where .the rst cavity is formed by the two obstacles :I'Bi

and the length of line S1 and the second cavity is formed by the obstacles y'B2 and the length of line S2. The third and fourth cavities are similar to the second and first cavities, respectively.

- The -irst and second cavities are connected by the .line S12, the second and third cavities by the fline S22 and the third and fourth cavities by S12.

The selectivity of the total lter is obtained from combining Equation 23 and Equation 21 :thus:

101.932) (1o)-'2QT1"=0.0371 26) Solving for QT Knowing the selectivity of the total lter, the

selectivities of the four cavities are determined byrEquation 1, thus:

Q2=Q3=89 sin 3%:822 Y (29) These selectivities are based upon the frequency. The selectivities based upon wavelengths are less by the factor AIas'pointed out above. Since the susceptances of the obstacles which form the cavities are given as aV function of the selectivity in terms of the' wavelength (Equation 11) and plotted thus in Fig. 6, the latter selectivities are thedesired ones and are from Equations 28 and 29 when the above correction factor is applied.

Since these cavities are to be connected by means of lines, whose selectivity corresponds the cavities are designed to have Qgfs that are:

This lter will then take 'voo ` lf,'as one example, the cavities are to be formed "with inductive obstacles as illustrated in Eig. or '13, the susceptances to obtain the above selectivities are obtained from Equation 1l or from curve Lk of Fig. l6. This vgives Y 1f these susceptances are to beobtained with round cylindrical posts centered in the wave guide, the data plotted in Fig. '7 can be useduto obtain the'required'post diameter with the aid Yof Equation 16.

Putting in the values of g=4-638 inchesand 2a=(1.8'72)(2)=3.744 inches we.v have, from v Equation 16,

.For B=-6.36, K=-5.15 and from Fig. 'z

and, therefore, d'2=o.1so inch.

The lengths of the cavities are determined by the' relationshipv (Equation 10) tain kan E which gives for vS1, setting Bri-4.08,

The `connectingvlengths S12. and S22, are determined from the relation (Equation 15):

which,V with mf=1, `reduces to from wihch A1. 2. su: E38-2i- 09 f V'I'hese calculated dimensions were usedtocon- .struct thelter shown in Fig. 11 except that all of the eight postsy I9, 22 were located onthe Vcenter line. `Each of the four cavities was tuned separately tothe resonant frequency by means of a capacitive screw I6 located'in the middle of each cavity. The resulting transmission characteristic was. :centered .two megacycles higher than fo. Retuning the cavities to ,fo-2 megacycles. and assembling them again, the

'characteristic Vshown in Fig. 9 was obtained experiment'ally.l The points 24, 25, 26 and 2l for the originaldesign objective are shown circled and itis seen that they agree fairly closely with the measured characteristic.

...asse-.488

T nlteriwounarene @encaminar-inistrated-.iin eFig. 11. Here all gfjthepQStsarefthejsame ties are moved farlflenoughfoff center, as shown in Figs. 11 and 12;;tofobtain the correct susceptance, B1=-4.08

@'-Ifthe obstacles' had been made f-uppfgplane inductive irises i such as `2 l1 illustrated in Fig.' 13, fthe# four-branch filter-would havehad the C Onfiguration shown-in Fig. 10. Ihe vflengths 81, S12, S2 and S22 would be the sameasfvfound for fFi'gf-llfand the iris openings couldI` have* been l -fde'termined as outlinedebefore;by-"use of-jiFKigsg and 8 and Equation 16 to obtain-thevalues-f B, K, di andida.

Had the four-branch elter been designed around capacitive obstacles, illustrated in Fig. 14g-the susceptances necessary-to-obtain* the required selectivitiescouldbe determined as before from Equation-'11 or curve C of Fig. 6. The susceptance would be controlled bytheiris vgapening zr, and the spacings ofthe elements Would* be determined,by:EquationsJllLandl f Thecapacitive obstacle shown in Fig. 14 comprises a transverse partition 28 withga centrally located rectangular aperture of width x extending completely across the frectangnlar 'wavejiguide Zzin direction. perpendicularfto;the=,e1ectrcvector E.

While the design` procedure;hasffbeenffcilowed through for the case of a four-branch lter incidental to illustratinggtheway in which a particular set of requirements could be met, the

lter designs A.of other numbers of required branches. This methodof-lter-'ffdesign has been successfully used to build filters-Whose specications required the employment kQfsfrom one to the mid-band frequency, the respective band Widths passed by said chainbersfbeing yapproximately-equalzto the-factor Yi-lere.' Tf'dGDQGQS :the Order; of@ the chamberacountfromione end ,offV the, filter .fandmiisffthe total number ,ofV chambers, andl adjacent chambers being -,Spaed .a distance approximatelypequalto thlegaverage spacing of thefpairsfofgadmittances -`,:leflning vsaid adjacent chambers,

Minus 4..and plusl ,70 where 'l is the wavelength insaid guide .,atQijsaid s diameter and the posts"l9'for`"'the two' end cavi- .3.5 Same kndefrfpmdurezean: beafelicvreditonbtain v .,340 fteen resonant cavities, andthe longer of these 3. A: ilterk inaccordance v with,Claim` 1 in. ,which hsaid admittances are capacitive.

4. A lter in accordance with claim1 inwhi said admittances are constituted by'irises.

1.5. A lter in accordancewith claim 1 in which V.said admittances are constituted by transverse partitions having apertures therein. Y

6. A filter in accordance with claim 5 inl-which said apertures infsaid pairs of partitions increase A`l lin size 'from'vthe centen to both ends fof l.said lter.

7. A lter in accordance with claim in which saidk apertures extend substantially all theway across saidguide ina direction parallel-to-'th electric vector of saidwaves.

18. `A vilter in accordance with claim 5 in which said apertures extend substantially all the way across said guide i in a direction perpendicular -to the t'electric vectorl of said waves. 4

9.1A'ii1terin accordance .with claim 1 in which l[gu-.said.admittances Vare constituted Ilby inductive postsextending allthe way .across said guide.

.10. A`lter in accordance with vrclaim 9 in which f all of said` posts are offsubstantiallyequal -crosssection and differenhpairs of saidpostsareposiftioned atdifferent distances from the long-ituj dinal center liney ofsaid guide. l

11. A filter in accordance with claim 10-in which the pairs, of posts dening the end chambers of the lter are located farther from said kk center line than are the intermediateposts.

12. A filter in accordance With claim 1 in which the susceptances of said pairs of admittances -decrease from the center Ato both -ends of 'said lten 13. A filter in accordance with -claim 1 --Which includes means fortuning said chambers.

-414. A lter irrfaccordance with claim 13 in which said meansomprise capacitive plugs in arwall of said .guide.

15. A ilter in accordance with claim 14 in which said plugs are parallel `to .the electric-vecto of said waves.

16. A microwave Afilter Ncomprising more than two resonant chambers tuned approximately to .15 the mid-band frequency, and interposed sections of wave guide connecting/'said chambers in tan- `-dern, therespectiveband widths passedl byfsaid ,chambers ,increasing progressively `from .the

.lcfenter to ,the endsof the'lter toproxidefa maximallyfflat transmission band -for rthellter.

v1'7. A{microwave iilterfcomprising more than ,twcresonan'l cllalilberSl tuned approximately, ,to

'the' mid-band ir'equencyand.interposed/sections of wave guide connecting said chambers in tandem, the respective band ,fwiidthsjvpassed by said chambers being approximately'proportional to the factor Minus and plus where l is the Wavelength-in said guide at said mid-band frequencyan'dm is any integer in- ',Q-ludinazeroi f 19. A lterior.transmittinga band of electromagnetic wavescomprising .a 4 igvave guide and Where A is the Wavelength in said guide at said mid-band frequency and m is any integer including zero.

2l. A wave guide filter comprising more than two resonant cavities spaced apart along awave guide by a distance approximately equal to an odd multiple, including unity, of quarter wavelengths at the resonant frequency and all having Minus and plus the same resonant frequency, said cavities increasing in bandwidth from the center of the l'ilter toward each end to provide a maximally-at transmission band characteristic.

22. A lter in accordance with claim 21 in which the V:spacing between said cavities is ad- 14 justed to compensate for the excess phase shift of ysaid cavities.

23. A filter in accordance With claim 16 in which said interposed sections of Wave guide are adjusted in length to compensate for the excess phase shift of said chambers.

24. A filter in accordance with claim 17 in which said interposed sections of wave guide are adjusted in length to compensate for the excess phase shift of said chambers.

WILLIAM W. MUNLEORD.

REFERENCES CITED The following references are of record in the file o1 this patent:

UNITED STATES PATENTS Number Name Date 1,849,556 Bennett Mar. 15, 1932 2,270,416 Cork Jan. 20, 1942 2,432,093 Fox Dec. 9, 1947 2,438,119 Fox Mar. 23, 1948 FOREIGN PATENTS Number Country Date 374,767 Italy Sept. 7, 1939 OTHER REFERENCES Fano and Lawson: Microwave lters using quarter-Wave couplings, I. R. E. Proceedings, vol. 35, No. 11, November 1947, pages 1318-1323. 178-44.2A.

Pritchard: Quarter wave coupled Wave-guide lters, Journal of Applied Physics, October 1947, pages 862-872. 

